Answer
$\pm 2.146$
Work Step by Step
We need to take natural log of both sides , then the given expression can be written as:
$\ln e^{x^2}=\ln 100 $
Apply logarithmic property : $\log a^ b=b \log a$ and $\ln e^a= a$
$x^2 =\ln 100$
Now, we will evaluate the result for $x$.
Therefore, our answer is: $x =\pm \sqrt {\ln 100}=\pm 2.146$